1. Detection
Capillary-based analysis schemes, biochemical analysis, basic research in the biological sciences such as localized pH determinations in tissues and studies in protein folding, detection and study of microorganisms, and the miniaturization of instrumentation down to the size of a chip all require small volume detection. With the advent of lasers, light sources possessing unique properties including high spatial coherence, monochromaticity and high photon flux, unparalleled sensitivity and selectivity in chemical analysis has become possible; these technologies, however, can be both expensive and difficult to implement. In contrast, refractive index (RI) detection has been successfully applied to several small volume analytical separation schemes. For various reasons, RI detection represents an attractive alternative to fluorescence and absorbance: it is relatively simple, it can be used with a wide range of buffer systems, and it is universal, theoretically allowing detection of any solute, making it particularly applicable to solutes with poor absorption or fluorescence properties.
However, there remains a need in the art for small and ultra-small volume detection methods that efficiently detect a shift between two or more signals while providing sub-pixel accuracy, thereby sensing temperature and flow rate of small and ultra-small volumes and/or detecting an analyte or a chemical event with very low detection limits.
2. Calculation
Auto-correlations and cross-correlations (“correlations”) have long been used to compare two functions, signals, data sets, or images. Most mathematics, signal processing, or data analysis software packages include correlations as built-in operators. These conventional techniques for computing cross-correlations only use the peak value of the cross-correlation to determine a shift between two signals, thereby limiting the resolution to plus-or-minus 1 sampling interval, increment, or pixel. Other conventional cross-correlation techniques involve transforming input signals into the frequency domain, such as by application of a Fourier transform, in order to calculate a shift.
There are also conventional techniques to compute a sub-pixel shift between two images that do not use correlations. However, these techniques are often too computationally intensive for application to real-time signal processing due to the many image differences they are designed to detect, measure, and correct.
Accordingly, there is a need in the art for methods, systems, apparatuses, and program products (hereinafter “methods”) that efficiently compute a shift between two or more signals, functions, data sets, or images while providing sub-pixel accuracy. Similarly, there is also a need in the art for sub-pixel cross-correlation methods that do not require transforming an input signal into the frequency domain.